A parcel of air with a volume of 9.1
The change in temperature of the parcel of air due to freezing.
Answer to Problem 4PEB
Solution:
Explanation of Solution
Given data:
The volume of parcel of air containing
Formula used:
Write the expression for thermal energy absorbed or released during the phase change of the substance.
Here,
Write the expression for density.
Here,
Rearrange the expression for density in terms of mass.
Write the expression for sensible heat.
Here,
Compare equation (2) and (3) and write the expression for sensible heat in terms of volume and density.
Explanation:
The parcel of air contains water vapour. At the condensation altitude, two stages of phase change occur. First, the water vapour condenses and change to liquid, and then it undergoes another phase change and freezes. The heat released from the two-phase change is absorbed by the surrounding air. The solution can be obtained in three steps.
Step 1: Consider the condition for the phase change when the water vapour undergoes condensation. The latent heat for vapourization of water vapour is
Here,
Substitute
Step 2: Consider the condition for the phase change when the condensed water vapour freezes further. The latent heat of fusion for water is
Substitute
Step 3: The heat released from the two-phase change is absorbed by the surrounding air. Therefore, the total heat released during the two-phase change is equal to the sensible heat. Calculate the total heat released during the phase change from water vapour to ice.
Substitute
This heat is equal to the sensible heat.
Therefore, calculate the change in temperature of the air parcel due to freezing.
Substitute
Conclusion:
The change in temperature due to freezing is
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